Identifying Linear Function

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, characterized by a constant rate of change.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed, meaning the rate of change is not constant.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in the y-values for equal intervals in the x-values.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-value to the change in the x-value, often represented as 'm' in the equation.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of 'b' in the equation f(x) = mx + b.

Front

What does it mean if a function has two outputs for the same input?

Back

If a function has two outputs for the same input, it is not a function according to the definition of a function.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which indicates that as the x-values increase, the y-values decrease.

Front

What is the difference between a linear and a nonlinear equation?

Back

A linear equation represents a straight line, while a nonlinear equation represents a curve or other shape that is not a straight line.